Heat the oil, lemon zest, garlic, red pepper, and ¼ teaspoon salt in a small pot over medium heat until sizzling, 2 to 3 minutes.
Prepare the grill. Place the clams and mussels on the grill. Grill, covered, without moving them, until the shells pop open and the meat is opaque throughout, 8 to 10 minutes for the clams and 3 to 7 minutes for the mussels.
Transfer to a large bowl. Add the chili-lemon oil and parsley and toss to combine. Serve with the bread.